12. (6 points) XYZ Life Insurance Company originates home equity loans to elderly
homeowners. The loan is not due for repayment until the borrower dies or moves out of
the property. The amount of the initial loan is based on the age of the borrower and the
property value. Interest and fees are accumulated until repayment. The only source of
repayment is the property.
A government institution provides insurance against the risk that the eventual repayment
amount is less than the loan balance at that time. The premium, which is added to the
loan balance, is an initial fee of 2% of the loan value and 0.5% of the outstanding loan
balance annually. The homeowner can repay in full at anytime without penalty.
The loan interest rate is reset every six months. The net rate of interest, after insurance
premium and expenses, is the rate on 6 month CD's plus 3%. Based on projected cash
flow, the company issues GICs of 1, 3 and 5-year maturities.
The following three strategies have been proposed:
(i) Issue fixed rate instead of variable rate loans.
(ii) Swap the variable interest rates for fixed interest rates.
(iii) Purchase insurance against the risk of homeowners dying earlier or later
than expected.
(a) Analyze the risks associated with the current strategy.
(b) Describe the risks associated with the three proposed strategies.
COURSE 8: Investment - 14 - STOP
November 2000
Morning Session
13. (7 points) You are given the following information about a European put option on a
non-dividend paying stock:
•Stock price 40
•Risk-free interest rate 7% (continuously compounded)
•Strike price 35
•Time to maturity 8 months
You are also given the following volatilities derived from actively-traded European call
options on the stock:
Strike Price
Time to maturity 30 35 40 45
3 months 0.290 0.225 0.180 0.150
6 months 0.280 0.230 0.230 0.160
1 year 0.275 0.236 0.221 0.180
(a) Calculate the price of this option using the Black-Scholes formula. Show your
work.
(b) Contrast the stock price distribution implied by the volatility matrix with the lognormal
distribution.
(c) Describe models of stock price behavior that are consistent with the implied
distribution.
14. (5 points) The asset portfolio of a U.S. life insurance company includes real estate
properties. The portfolio manager is currently considering adding to the portfolio an
equity investment in an office building in Atlanta. The building is fully leased at fixed
rates with 10 years remaining on its leases and subject to a mortgage equal to 50% of its
current market value. The mortgage is for 10 years, interest-only, and interest is paid
monthly at 1 month LIBOR plus a fixed spread.
(a) Evaluate the risks of this specific investment.
(b) Propose approaches to reduce the risks identified in (a).
COURSE 8: Investment - 15 - STOP
November 2000
Morning Session
15. (7 points) The debt of Company X consists of one zero coupon bond with the following
payment probabilities at maturity:
Default Risk Probabilities
Real World Risk-Neutral
No default 85% 75%
Default with 70% recovery 10% 15%
Default with 35% recovery 5% 10%
Additional information is as follows:
•Debt maturity 5 Years
•Payment due at maturity 1000
•Risk-free rate 5% (continuously compounded)
Company Z has written a European option which will pay 1000 in 5 years in exchange
for Company X’s debt.
Assume Company X and Z have equal but independent default risk.
(a) Calculate the market's expected spread for the bond over the risk-free rate. Show
your work.
(b) Determine the possible payoffs at maturity of a European option written by
Company Z which will pay 1000 in 5 years in exchange for Company X's debt.
(c) Calculate the value of this option. Show your work and state your assumptions.
COURSE 8: Investment - 16 - STOP
November 2000
Morning Session
16. (6 points) You are given the following information about two estimations of the Market
Value (MV) of the total policy liabilities of a life insurance company:
Method used Estimation
MV (Liability) $2.0 billion
MV (Asset) – MV (Equity) $1.8 billion
(a) Contrast the two methods.
(b) Explain how the uncertainty of cash flows can be reflected in the estimation of the
market value under the MV (Liability) method.
17. (5 points)
(a) Describe the following fixed income risk measures:
(i) prepayment uncertainty,
(ii) volatility risk (vega),
(iii) zero volatility spread (ZVO),
(iv) spread duration.
(b) Your company’s fixed income portfolio contains MBS, CMBS, CMO, ARM,
callable and putable corporate bonds, and ABS. Explain the impact of each of the
risk measures above on the different fixed income asset classes.
** END OF EXAMINATION **
AFTERNOON SESSION

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